Rather than use the stencil buffer to mask out the region outside the
reflector, if the mirror polygon has five or fewer edges (four is a
common number), OpenGL's clip planes can be configured to clip the
reflected geometry to the region directly behind the mirror polygon.

For each edge, calculate the plane that is formed by that edge and the
eyepoint. Configure this plane as a clip plane (without applying the
reflection transformation). Finally, configure one plane to clip
reflected polygons to the plane of the reflector, as in the stencil
technique.

This may be a viable alternative if hardware does not support a
stencil buffer.